An Indian community group in Auckland wants an apology from Shane Jones over comments he directed at people unhappy with changes to immigration policy.
The New Zealand First MP and Cabinet minister said if the Indian community wasn't happy with the changes, they should get on the first plane home.
A change in approach by immigration officials to partnership visas means Indians in particular are having a much harder time bringing their spouses to New Zealand.
There has been a specific government directive to stop waiving requirements such as couples needing to have lived together for 12 months - a test Indian couples who have had arranged marriages can't meet.
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Talking about a more recent change to the parent category visa last weekend, Mr Jones told RNZ he was saddened by the "levels of verbiage that the Indian communal leadership have thrown at the party".
"I would just say to the activists from the Indian community, tame down your rhetoric, you have no legitimate expectations in my view to bring your whole village to New Zealand and if you don't like it and you're threatening to go home - catch the next flight home."
The Waitākere Indian Association said the comments were insensitive and should be condemned.
It wants the prime minister, the Minister of Ethnic Communities, the opposition and sitting Indian MPs to support its demand for a public apology from Mr Jones.
The association also urged the Immigration Minister Iain Lees-Galloway and Minister of Ethnic Communities Jenny Salesa to engage with the community to understand cultural differences and work towards a solution to incorporate it into immigration policy.
There was a sense of despair among Indians living in New Zealand that the recently announced income thresholds to apply for a parent visa are so high, the association said.